Related papers: Composites In Semirings of Boolean Groups
Our main goal is to develop a representation for finite distributive nearlattices through certain ordered structures. This representation generalizes the well-known representation given by Birkhoff for finite distributive lattices through…
We are interested in formulas for the number of elements in certain classes of numerical semigroups
Every mathematician is familiar with the beautiful structure of finite commutative groups. What is less well known is that finite commutative semigroups also have a neat and well-described structure. We prove this in an efficient fashion.…
In this short note we count the finite semirings up to isomorphism, and up to isomorphism and anti-isomorphism for some small values of $n$; for which we utilise the existing library of small semigroups in the GAP package Smallsemi.
We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…
We describe the structure of finite Boolean inverse monoids and apply our results to the representation theory of finite inverse semigroups. We then generalize to semisimple Boolean inverse semigroups.
Since for the classification of finite (congruence-)simple semirings it remains to classify the additively idempotent semirings, we progress on the characterization of finite simple additively idempotent semirings as semirings of…
A semiring generalises the notion of a ring, replacing the additive abelian group structure with that of a commutative monoid. In this paper, we study a notion positioned between a ring and a semiring -- a semiring whose additive monoid is…
A well-known theorem of Wedderburn asserts that a finite division ring is commutative. In a division ring the group of invertible elements is as large as possible. Here we will be particularly interested in the case where this group is as…
In this paper we compute the set of point modules of finitely semi-graded rings. In particular, from the parametrization of the point modules for the quantum affine n-space, the set of point modules for some important examples of non…
In this paper, we study the proportion of vanishing elements of finite groups. We show that the proportion of vanishing elements of every finite non-abelian group is bounded below by $1/2$ and classify all finite groups whose proportions of…
In this paper, we introduce and investigate \emph{semicorings} over associative semirings and their categories of \emph{semicomodules.} Our results generalize old and recent results on corings over rings and their categories of comodules.…
We obtain the formula computing the number of isomorphic classes of element systems with characters over finite commutative group $G$.
We study Kostant's partial order on the elements of a semisimple Lie group in relations with the finite dimensional representations. In particular, we prove the converse statement of [3, Theorem 6.1] on hyperbolic elements.
Commutative semirings with divisible additive semigroup are studied. We show that an additively divisible commutative semiring is idempotent, provided that it is finitely generated and torsion. In case that a one-generated additively…
We investigate the class of quasitrivial semigroups and provide various characterizations of the subclass of quasitrivial and commutative semigroups as well as the subclass of quasitrivial and order-preserving semigroups. We also determine…
In this paper, we describe finite, additively commutative, congruence simple semirings. The main result is that the only such semirings are those of order 2, zero-multiplication rings of prime order, matrix rings over finite fields, those…
A finite semifield $D$ is a finite nonassociative ring with identity such that the set $D^*=D\setminus\{0\}$ is closed under the product. In this paper we obtain a computer-assisted description of all 64-element finite semifields, which…
Irreducible decompositions of monomial ideals in polynomial rings over a field are well-understood. In this paper, we investigate decompositions in the set of monomial ideals in the semigroup ring A[\mathbb{R}_{\geq 0}^d] where A is an…
The main purpose of this paper is to investigate the zero-divisors of semigroups with zero and semirings and in particular, to discuss eversible and reversible semigroups and semirings. We also introduce a new ring-like algebraic structure…